A New Frailty Model Based Archimedean Bivariate Copula That Models Only Positive Dependency

In this paper, the author utilizes the frailty model to construct a new Archimedean copula. This copula depends on the transformed Median Based Unit Rayleigh (MBUR) distribution to unbounded distribution defined on the interval from zero to infinity. The copula only models the positive dependency. In the paper, the joint PDF and CDF of the copula are derived for two bivariate distributions. The singularity of the copula is explained. The generator and inverse generator of the new copula are explored with various graphs to depict the decreasing and convex nature of the generator with different dependency parameter values. The Kendall tau measure of dependency is derived. For this copula, the lower and upper tail dependencies exist. The formula for each one is derived. This new copula is one of the parametric Archimedean copulas. Unfortunately, the Archimedean copulas are not widely used.